QUELQUES PROPRIÉTÉS EXTRÉMALES DES VALEURS SINGULIÈRES
D’UN OPÉRATEUR COMPACT ET LEURS APPLICATIONS AUX
ANALYSES FACTORIELLES D’UNE PROBABILITÉ OU D’UNE FONCTION
ALÉATOIRE
I. QUELQUES PROPRIÉTÉS EXTRÉMALES DES VALEURS SINGULIÈRES
D’UN OPÉRATEUR COMPACT
Alain Pousse
Jean-Jacques Téchené
Abstract: We give global criteria for the canonical reductions of an unnecessary self-adjoint
operator on a complex separable Hilbert space. These criteria are obtained by an extension of
the Poincaré separation theorem for the eigenvalues of a Hermitian matrix. We derive
extremal properties of the singular values of a compact operator, thus generalizing known
results in finite dimension (cf. [3], [10], [11]) and the recent results by Göhberg and Krejn
[7]. Our goal is to find criteria for the factor analysis of a probability defined on a separable
Hilbert space or of a real random function other than a finite or countable set of real random
variables.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -